Nonlocal Behavior Research Articles

Nonlocality free wirings and the distinguishability between Bell boxes

Bell nonlocality can be formulated in terms of a resource theory with local-hidden variable models as resourceless objects. Two such theories are known, one built upon local operations assisted by shared randomness (LOSRs) and the other one allowing, in addition, for prior-to-input classical communication. We show that prior communication, although unable to create nonlocality, leads to wirings not only beyond LOSRs but also not contained in a much broader class of (nonlocality-generating) global wirings. Technically, this is shown by proving that it can improve the statistical distinguishability between Bell correlations optimised over all fixed measurement choices. This has implications in nonlocality quantification, and leads us to a natural universal definition of Bell nonlocality measures. To end up with, we also consider the statistical strength of nonlocality proofs. We point out some issues of its standard definition in the resource-theoretic operational framework, and suggest simple fixes for them. Our findings reveal non-trivial features of the geometry of the set of wirings and may have implications in the operational distinguishability of nonlocal behaviors.

A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams

In this paper, size dependent bending and free flexural vibration behaviors of functionally graded (FG) nanobeams are investigated using a nonlocal quasi-3D theory in which both shear deformation and thickness stretching effects are introduced. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present theory incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a hyperbolic variation of all displacements through the thickness without using shear correction factor. The material properties of FG nanobeams are assumed to vary through the thickness according to a power law. The neutral surface position for such FG nanobeams is determined and the present theory based on exact neutral surface position is employed here. The governing equations are derived using the principal of minimum total potential energy. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and dynamic responses of the FG nanobeam are discussed in detail. A detailed numerical study is carried out to examine the effect of material gradient index, the nonlocal parameter, the beam aspect ratio on the global response of the FG nanobeam. These findings are important in mechanical design considerations of devices that use carbon nanotubes.

Nonlocal modeling of a randomly distributed and aligned long-fiber composite material

The work under study is about the variational and stochastic modeling of randomly distributed and aligned long-fiber composites. Its objective is to derive a homogenized behavior that exhibits the nonlocal phenomenon of this type of material at the macroscopic scale. Several methods of applied mathematics are used in order to keep the maximum information about the nonlocal behavior after homogenization.

Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism

This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from non-equilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of sub-grid models is considered which represent non-local behavior via a finite memory approximation (Stinis, P., "Mori-Zwanzig reduced models for uncertainty quantification I: Parametric uncertainty," \textit{arXiv:1211.4285}, 2012.), the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase-space is accurately predicted for cases where the coarse-graining is moderate. LES of homogeneous isotropic turbulence and the Taylor Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the sub-grid contribution to energy transfer. Lastly, LES of fully developed channel flow demonstrate the applicability of M-Z-based models to non-decaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse-graining, highlighting the potential of M-Z-based techniques to define LES closures.

Electro-magnetic effects on nonlocal dynamic behavior of embedded piezoelectric nanoscale beams

This article investigates vibration behavior of magneto-electro-elastic functionally graded nanobeams embedded in two-parameter elastic foundation using a third-order parabolic shear deformation beam theory. Material properties of magneto-electro-elastic functionally graded nanobeam are supposed to be variable throughout the thickness based on power-law model. Based on Eringen’s nonlocal elasticity theory which captures the small size effects and using Hamilton’s principle, the nonlocal governing equations of motions are derived and then solved analytically. Then, the influences of elastic foundation, magnetic potential, external electric voltage, nonlocal parameter, power-law index, and slenderness ratio on the frequencies of the embedded magneto-electro-elastic functionally graded nanobeams are studied.

Partial jamming and non-locality in dense granular flows

Dense granular flows can exhibit non-local flow behaviours that cannot be predicted by local constitutive laws alone. Such behaviour is accompanied by the existence of diverging cooperativity length. Here we show that this length can be attributed to the development of transient clusters of jammed particles within the flow. By performing DEM simulation of dense granular flows, we directly measure the size of such clusters which scales with the inertial number with a power law. We then derive a general non-local relation based on kinematic compatibility for the existence of clusters in an arbitrary non-homogenous flow. The kinematic nature of this derivation suggests that non-locality should be expected in any material regardless of their local constitutive law, as long as transient clusters exist within the flow.

Static behavior of nonlocal Euler-Bernoulli beam model embedded in an elastic medium using mixed finite element formulation

The size-dependent behavior of single walled carbon nanotubes (SWCNT) embedded in the elastic medium and subjected to the initial axial force is investigated using the mixed finite element method. The SWCNT is assumed to be Euler- Bernoulli beam incorporating nonlocal theory developed by Eringen. The mixed finite element model shows its great advantage of dealing with nonlocal behavior of SWCNT subjected to a concentrated load owing to the existence of two coefficients alpha1 and alpha2. This is the first numerical approach to deal with a puzzling fact of nonlocal theory with concentrated load. Numerical examples are performed to show the accuracy and efficiency of the present method. In addition, parametric study is carefully carried out to point out the influences of nonlocal effect, the elastic medium, and the initial axial force on the behavior of the carbon nanotubes.

Wall roughness and nonlinear velocity profiles in granular shear flows

Inhomogeneous velocity profiles in granular flows are well known from both experiments and simulations, and considered as a hallmark of nonlocal behavior. By means of extensive contact dynamics simulations, we show that the sigmoidal velocity profiles in 2D flows of rigid disks are controlled by the roughness of driving boundary walls. We find that the velocity profile becomes linear for a critical value of wall roughness up to an exponential decay close to the walls with a characteristic length that does not depend on the flow thickness and rate. We describe the velocity profiles by introducing a state parameter that carries wall perturbation. By assuming that the local shear rate is a linear function of the state parameter, we obtain an analytical expression that fits velocity profiles. In this model, the nonlinear velocity profiles are explained in terms of the effects of wall roughness as boundary condition for the state parameter.

Discharge stratification in noble gases as convergence of electron phase trajectories to attractors

A new dynamic method to analyse resonance effects in glow discharges is proposed as a supplement to fluid and kinetic approaches for the investigation of discharge stratification. The method is applicable to striations, which are caused by the nonlocal electron behaviour at lower pressure and current. It is based on the analysis of the electron phase trajectories in spatially periodic fields. Being quite intuitive and easier than the solution of the Boltzmann equation, this method gives a quantitative description of the main effects arising from the kinetic analysis, for example, the appearance of attractors of the phase trajectories. The dynamic theory eliminates the main difficulty of the kinetic theory associated with the large relaxation length of the electron energy distribution function in periodic fields and describes the integer and rational resonances that correspond to S-, P- and R-striations. As a result, the stratification of the discharge can be interpreted as the excitation of one of the spatial resonator modes of the positive column.

Influence of yttrium iron garnet thickness and heater opacity on the nonlocal transport of electrically and thermally excited magnons

We studied the nonlocal transport behavior of both electrically and thermally excited magnons in yttrium iron garnet (YIG) as a function of its thickness. For electrically injected magnons, the nonlocal signals decrease monotonically as the YIG thickness increases. For the nonlocal behavior of the thermally generated magnons, or the nonlocal spin Seebeck effect (SSE), we observed a sign reversal which occurs at a certain heater-detector distance, and it is influenced by both the opacity of the YIG/heater interface and the YIG thickness. Our nonlocal SSE results can be qualitatively explained by the bulk-driven SSE mechanism together with the magnon diffusion model. Using a two-dimensional finite element model (2D-FEM), we estimated the bulk spin Seebeck coefficient of YIG at room temperature. The quantitative disagreement between the experimental and modeled results indicates more complex processes going on in addition to magnon diffusion and relaxation, especially close to the contacts.

Heat conduction with fractional Cattaneo–Christov upper-convective derivative flux model

Fractional order derivatives are global operators for which the time fractional order derivative possesses memory character while the space ones reflects non-local behavior. In this paper, a new time and space fractional Cattaneo–Christov upper-convective derivative flux heat conduction model is suggested where the space fractional derivative is characterized by the weight coefficient of forward versus backward transition probability. Governing equation is formulated and solved by L1-approximation and shifted Grünwald formula. Results show that the fractional parameters, time and location parameters, relaxation parameter, weight coefficient and convection velocity have remarkable impacts on heat transfer characteristics. Temperature distribution profiles are monotonically decreasing in a concave form versus time fractional parameter with existing of relaxation parameter, while in a convex form with space fractional parameter evolution under three special conditions, i.e., the right region, the larger weight coefficient (γ ≥ 0.5) and smaller convection parameter u.

Perturbation theory in supersymmetric QED: Infrared divergences and gauge invariance

We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.

On the nonlocality of the Coulomb gauge external field problem

The apparent nonlocality of the Coulomb gauge external field problem in electrodynamics is illustrated with an example in which nonlocality is especially striking. Explanation of this apparent nonlocal behaviour based on a purely local picture is given. A gauge invariant decomposition of the Lorentz-force into two terms with clear physical meanings is pointed out. Based on this decomposition derivation of the Aharonov–Bohm effect in terms of field strengths alone is given.

A relaxation‐based approach to damage modeling

AbstractCommon material models that take into account softening effects due to damage have the problem of ill‐posed boundary value problems if no regularization is applied. This condition leads to a non‐unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this problem is to apply regularization techniques that take into account the non‐local behavior of the damage [1]. For this purpose a field function is often used to couple the local damage parameter to a non‐local level, in which differences between the local and non‐local parameter as well as the gradient of the non‐local parameter can be penalized. In contrast, we present a novel approach [2] to regularization that no longer needs a non‐local level but directly provides mesh‐independent results. Due to the new variational approach we are also able to improve the calculation times and convergence behavior. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Nonlocal type asymptotic behavior for solutions of second order difference equations

In this work we consider a discrete nonlocal problem of the following type: $$\textstyle\begin{cases} \Delta ( q \Delta \mathbf {x} )(n) + f (n+1, \mathbf {x}(n+1) ) =0, \mathbf {x}(\infty) = g(\mathbf {x}), \end{cases} $$ in the context of an arbitrary Banach space $(X,\lVert\cdot\rVert _{X})$ , and we give sufficient conditions that ensure the existence of solutions to it. In order to present our result, we shall need to study conditions that ensure the existence of solutions with a nonlocal asymptotic behavior for the following equation: $$\mathbf {x}(n) = g(\mathbf {x}) - \sum_{k=n+1}^{\infty}\sum_{j=n}^{k-1} \frac{1}{q(j)} f \bigl(k, \mathbf {x}(k) \bigr). $$

Non-local theory behavior of multiple cracks in a functionally graded piezoelectric medium

In this paper, the non-local theory solution of multiple cracks in a functionally graded piezoelectric medium (FGPM) under the permeable electric boundary condition have been investigated. Overcoming the mathematical difficulty, a one-dimensional non-local kernel is used instead of a two-dimensional one for the fracture problem to obtain stress and electric displacement fields near the crack tips. By using Fourier transform techniques, the present problem was reduced to the solution of dual integral equations, which unknown variable is jumps of displacement across the crack surface. The present solution exhibits no stress and electric displacement singularities at the crack tips when non-local was used to investigate the problem. The non-local solution yields a finite hoop stress at the crack tips, thus allows us to use the calculated maximum stress as a fracture criterion.

Influence of thermal and surface effects on vibration behavior of nonlocal rotating Timoshenko nanobeam

This paper is proposed to study the free vibration of a rotating Timoshenko nanobeam based on the nonlocal theory considering thermal and surface elasticity effects. The governing equations and the related boundary conditions are derived using the Hamilton’s principle. In order to solve the problem, generalized differential quadrature method is applied to discretize the governing differential equations corresponding to clamped–simply and clamped–free boundary conditions. In this article, the influences of some parameters such as nonlocal parameter, angular velocity, thickness of the nanobeam, and thermal and surface elasticity effects on the free vibration of the rotating nanobeam are investigated, and the results are compared for different boundary conditions. The results show that the surface effect and the nonlocal parameter and the temperature changes have significant roles, and they should not be ignored in the vibrational study of rotating nanobeams. Also, the angular velocity and the hub radius have more significant roles than temperature change effects on the nondimensional frequency. It is found that the nonlocal parameter behavior and the temperature change behavior on the frequency are different in the first mode for the rotating cantilever nanobeam.

Triple pendulum model involving fractional derivatives with different kernels

The aim of this work is to study the non-local dynamic behavior of triple pendulum-type systems. We use the Euler-Lagrange and the Hamiltonian formalisms to obtain the dynamic models, based on the Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu-Caputo fractional derivative definitions. In these representations, an auxiliary parameter σ is introduced, to define the equations in a fractal temporal geometry, which provides an entire new family of solutions for the dynamic behavior of the pendulum-type systems. The phase diagrams allow to visualize the effect of considering the fractional order approach, the classical behavior is recovered when the order of the fractional derivative is 1.

Clauser-Horne/Eberhard Inequality Violation by a Local Model

The Clauser-Horne/Eberhard inequality has taken center stage in tests of locality thanks to its immunity to the detection loophole. I describe a local model that violates the inequality using a plausible mechanism relying upon a parameter of the apparatus, the emission rate. The effect is generated through the analysis of time-tagged data using a standard windowed coincidence method; however, the detection times are not functions of the measurement settings. The analysis does not introduce the nonlocal behavior typical of previous coincidence window models. This finding has implications for the design and interpretation of experiments, as it shows that the coincidence window loophole cannot be eliminated by a demonstration of independence of the detection times and settings. The paper describes a reliable coincidence counting method and shows that it delivers an accurate count of true coincidences. Recent experimental tests of local realism based on the Clauser-Horne/Eberhard inequality are considered and it is shown that in one case (Christensen et al.) the emission rate is appropriately limited to ensure valid counting, and the data confirms local realism; in a second case (Giustina et al.) the experiment fails to appropriately limit the emission rate, and the claimed violation can be accounted for locally.

Thermal rectification based on phonon hydrodynamics and thermomass theory

Abstract The thermal diode is the fundamental device for phononics. There are various mechanisms for thermal rectification, e.g. different temperature dependent thermal conductivity of two ends, asymmetric interfacial resistance, and nonlocal behavior of phonon transport in asymmetric structures. The phonon hydrodynamics and thermomass theory treat the heat conduction in a fluidic viewpoint. The phonon gas flowing through the media is characterized by the balance equation of momentum, like the Navier-Stokes equation for fluid mechanics. Generalized heat conduction law thereby contains the spatial acceleration (convection) term and the viscous (Laplacian) term. The viscous term predicts the size dependent thermal conductivity. Rectification appears due to the MFP supersession of phonons. The convection term also predicts rectification because of the inertia effect, like a gas passing through a nozzle or diffuser.